Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras
@article{Oh2019TwistedAF, title={Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras}, author={Se-jin Oh and Uhi Rinn Suh}, journal={Journal of Algebra}, year={2019} }
12 Citations
Continuous Quivers of Type A (II) The Auslander-Reiten Space
- Mathematics
- 2019
This work is the sequel to Continuous Quivers of Type A (I). In this paper we define the Auslander-Reiten space of a continuous type $A$ quiver, which generalizes the Auslander-Reiten quiver of typeβ¦
Q-data and Representation Theory of Untwisted Quantum Affine Algebras
- MathematicsCommunications in Mathematical Physics
- 2021
For a complex finite-dimensional simple Lie algebra g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}β¦
PBW theory for quantum affine algebras
- Mathematics
- 2020
Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of arbitrary type and let $\mathcal{C}_{\mathfrak{g}}$ be Hernandez-Leclerc's category. We can associate the quantum affine Schur-Weyl dualityβ¦
Isomorphisms among quantum Grothendieck rings and propagation of positivity
- Mathematics
- 2022
Abstract Let (π€,π){\mathfrak{g},\mathsf{g})} be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with π{\mathsf{g}} being of simply-lacedβ¦
Categorical crystals for quantum affine algebras
- MathematicsJournal fΓΌr die reine und angewandte Mathematik (Crelles Journal)
- 2022
Abstract In this paper, a new categorical crystal structure for the quantum affine algebras is presented. We introduce the notion of extended crystals B ^ π€ β’ ( β )β¦
Block decomposition for quantum affine algebras by the associated simply-laced root system
- Mathematics
- 2020
Let $U_q'(\mathfrak{g})$ be a quantum affine algebra with an indeterminate $q$ and let $\mathscr{C}_\mathfrak{g}$ be the category of finite-dimensional integrable $U_q'(\mathfrak{g})$-modules. Weβ¦
Toroidal Grothendieck rings and cluster algebras
- MathematicsMathematische Zeitschrift
- 2021
We study deformations of cluster algebras with several quantum parameters, called toroidal cluster algebras, which naturally appear in the study of Grothendieck rings of representations of quantumβ¦
PBW theoretic approach to the module category of quantum affine algebras
- MathematicsProceedings of the Japan Academy, Series A, Mathematical Sciences
- 2021
Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of untwisted affine ADE type and let $\mathcal{C}^0_{\mathfrak{g}}$ be Hernandez-Leclerc's category. For a duality datum $\mathcal{D}$ inβ¦
Simply laced root systems arising from quantum affine algebras
- MathematicsCompositio Mathematica
- 2022
Let $U_q'({\mathfrak {g}})$ be a quantum affine algebra with an indeterminate $q$, and let $\mathscr {C}_{\mathfrak {g}}$ be the category of finite-dimensional integrable $U_q'({\mathfrakβ¦
The (q,Β t)-Cartan matrix specialized at $$q=1$$ q = 1 and its applications
- MathematicsMathematische Zeitschrift
- 2023
The ( q ,Β t )-Cartan matrix specialized at $$t=1$$ t = 1 , usually called the quantum Cartan matrix , has deep connections with (i) the representation theory of its untwisted quantum affine algebra,β¦
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